THE MYSTERY OF THE LINE OF BEARING
By Rear Admiral G. H. Burrage, U. S. Navy
One of the troubles of the officer of the deck in formation is to understand the fundamental principle of getting into position in line of bearing and when out of position what to do to get back.
See Fig. 1. A is the guide, B is the correct position in line of bearing. B1, B2, and B3 are positions inside the distance and ahead of the bearing, which is all the information the officer of the deck is given. Each case has to be handled differently. All slow down but B1 shears to right, B2 keeps her course, B3 sheers to left.
B4, B5 and B6 are positions outside of the distance and behind the line of bearing and like the above, the solution differs in each case. All increase speed—B4 sheers to right, B5 keeps her course, B6 sheers to left.
See Fig. 2. A is the guide, B is the correct position in the line of bearing. B1 and B2 are outside the distance and ahead of the bearing. Both sheer to the left, but B1 has to speed up and B2 slow down.
See Fig. 3. A is the guide, B is the correct position in line of bearing, B1, B2 are both inside the distance but B1 is ahead of the bearing and B2 behind, yet both do the same, slow down and sheer to the right.
See Fig. 4. A is the guide, B is the correct position in the line of bearing. The fundamental principle is to separate the distance and bearing from the guide into its component parts at right angles (B-C) and parallel (B-D) to the course of the guide. By keeping the distance B-C approximately correct, then it is simply a question of changes of revolutions to keep position; in other words, first keep on the line B-D, then correct bearing by slowing or increasing speed.
See Fig. 5. A is the guide, B is the correct position in the line of bearing. Draw a vertical line B-C on the mooring board through the correct position B on the line of bearing, parallel to the course of the guide. With the bearing and distance of the guide the junior officer of the deck plots the position B1 and gives the distance B1D from the vertical line B-C. A ruler marked to the desired scale, in yards, simple to construct, pivoted in the center of the mooring board will give the position B1 in a few seconds and the distance B1D.
One of the things to remember is that the officer of the deck must not try to do all the things himself, that he is provided with assistants to help him produce results.
See Fig. 6. A is the guide, B and C are the correct positions in the line of bearing. Remember that in a one point bearing B, a small error of bearing B1 makes a big error in distance, B1A, from the guide, when on the correct vertical line. There is great temptation when the distance decreases to sheer out from the guide. A ten degree change of course and no change of speed will land B1 in the position B2 4 ½ minutes if standard speed is 10 knots.
If the standard speed is 20 knots it will take but 2 ¼ minutes for B1 to reach position B2, with a 10 degree change of course.
Attention is particularly called to the fact that when near the correct bearing and with a large error in distance; change in speed is the answer, on the 15 degree bearing, as at B1; and change in course for the 90 degree bearing as at Co.
See Fig. 7. When on the 90 degree bearing and correcting your distance you are warned of the danger of too great a change in course as you may be caught with a signal to go ships right or left and the signal of execution within a few seconds of the signal being made; without giving you a chance to straighten out on your course and a situation as figure 7 develops.
A is the guide and promptly puts her helm over at the hauling down of the signal to go ships right 90 degrees and at 15 knots arrives at position A1 in 40 seconds.
B has been closing in at 20 degrees change in course and reaches position B1 before beginning to turn.
Not only a risk of collision between A and B but B will find herself very much out of position.
See Fig. 8. An interesting study of how to change position B1 to B2 and remain on the line of bearing, AB1B2.
Speed of guide, A, 20 knots.
On the mooring board draw a line through the speed of the guide (20 knots) point parallel to the line B1B2, and where it cuts the 19 knot curve at C gives 3 degrees, which means that B1 reduces speed to 19 knots and changes course to the right 3 degrees to keep on the line of bearing AB1B2.
The following table gives the change of course for different speeds taken from Fig. 8:
Line cuts 19 knot circle at C gives 3 degrees change of course
Line cuts 18 knot circle at D gives 6 ½ degrees change of course
Line cuts 17 knot circle at E gives 11 ½ degrees change of course
Line cuts 16 knot circle at F gives 17 degrees change of course
Line cuts 15 knot circle at G gives 25 degrees change of course
(Slowest speed possible) Line cuts 14 2/10 knot circle at H gives 45 degrees change of course
Line cuts 20 knot circle at B3 gives 90 degrees change of course
In deciding upon what change of course and consequent change of speed to go from one position to another, due regard must be had for the distance to be gained from right or left of your present position.
For example, see Fig. 8. To go from B1 to B2 or anywhere on that line of bearing where the line parallel to the line B1B2 cuts the speed of the guide at A (20 knots) gives 90 degrees, but manifestly if you were to gain 100 yards to the right you would not attempt to turn 90 degrees and steam 20 knots but you would do it if you had to gain 5000 yards.
The speed at right angles to the course of the guide is obtained as follows:
See Fig. 8. Take for example, you have decided to slow down to 16 knots. You find the 16 knot circle cuts the line A1 B3, which is parallel to the line B1B2. through the point A1, the speed of the guide, at F which gives a change of course of 17 degrees. Resolve the speed A-F parallel to the course of the guide A1, and at right angles to the course of the guide F-13 and the length of the line F-13 measured on the scale of knots gives 5 knots, which means that when B1 slows down to 16 knots, changes course to the right 17 degrees, she advances parallel to the course of the guide A at 15 knots, and at right angles to the course of the guide 5 knots.
If the distance B1K you have to gain to the right is 1000 yards, you go in the direction B1K at the speed of 5 knots, or 500 yards in three minutes, 1000 yards in six minutes.
All of this information is obtained from the mooring board.
See Fig. 9. A is the guide. Remember in changing from a stern B, to a 45 degree bearing, C, the distance A-D has to be gained to the right but the changing from a 45 degree bearing, C, to a beam bearing, E, the same number of degrees as before, only the distance D-E has to be gained.
See Fig. 10. When keeping position in line of bearing, set the pelorus for the correct bearing, B-30, and watch if the correct bearing is moving ahead or astern. If moving ahead then to bring the line back on the guide, slow down.
It is important to keep to this method, as it not only tells what is to be done to regain position but gives an estimate of how many yards out of position you are.
For example; if the line cuts the jack staff, you know you are the length of the forecastle out of position, 50 yards or whatever the length of the forecastle may be.
If you depend upon the actual bearing to give you the information to keep your position and; for example, if the correct bearing is 30 degrees and your bearing is 27 degrees, what to do to change 27 degrees to 30 degrees is the problem that presents itself to your mind. The temptation is to reason you have to add to your speed to go from 27 degrees to 30 degrees and many experienced officers have made that mistake.
Where does the correct line of bearing cut? Ahead of the guide brings the direct reasoning, slow down to bring the line back on the guide.
Fig. 11, a section of the mooring board, is constructed on the same principle as shown in Fig. 8, for every 10 degree line of bearing and the results tabulated. For 10 knot standard speed one knot maximum change in speed, 10 degree maximum change of course in Fig. 12.
For 20 knot standard speed. 2 knot maximum change in speed. 5 degree maximum change of course, in Fig. 13.
The method of using Fig. 11. To go from B-11 to B, using not more than 10 degree change in course with 10 knot standard speed. The line B-11 B if extended cuts the 10 degree radius at D which is on the 10 9/10 knot circle; which means for a change of course of 10 degrees a change of speed to 10 9/10 knots.
If no more than 5 degrees change in course. The line B-11 cuts the 5 degree radius at E on the 10 4/10 knot circle which means for a change of course of 5 degrees a change of speed to 10 4/10 knots.
To go from B to B13, 20 knot standard speed, not more than 10 degrees change in course.
The line B-B13 cuts the 18 knot circle at F on the 8 degree radius and the 5 degree radius at G on the 18.7 knot circle, meaning that with a change of course of 8 degrees you change your speed to 18 knots; with a change in course of 5 degrees you change your speed to 18.7 knots.
The distance of F from the vertical line F-H at the scale of knots gives 2.5 knots, is the speed at right angles to the course of the guide.
Figs. 12 and 13. B is your correct position in any line of bearing and taking a maximum error of 10 degree yards and every 10 degrees on the 100 yard circle the change in speed and change m course with resulting time to regain correct position, B, is tabulated, with the intention of impressing on you the fact that with 100 yards error of position how quickly your position is regained.
See Fig. 14. A F is the original course. A D a change of course of 30 degrees. A D resolves at right angles A C to the original course. A F shows that you go to the right at one-half your original speed.
This means that if your speed in the direction A F is 20 knots and you change your course 30 degrees you will go in the direction A C at the rate of 10 knots.
The Nautical Eye and Nautical Judgment must he Developed Through Knowledge.